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A Survey of Numerical Mathematics Volume 1

David M. Young and Robert T. Gregory
Dover Publications
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Chapter 1 Numerical Analysis as a Subject Area
 1.1 Introduction
 1.2 Some pitfalls in computation
 1.3 Mathematical and computer aspects of an algorithm
 1.4 Numerical instability of algorithms and ill-conditioned problems
 1.5 Typical problems of interest to the numerical analyst
 1.6 Iterative methods
Chapter 2 Elementary Operations with Automatic Digital Computers
 2.1 Introduction
 2.2 Binary arithmetic
 2.3 Conversion from base D to base B representation
 2.4 Representation of integers on a binary computer
 2.5 Floating-point representations
 2.6 Computer-representable numbers
 2.7 Floating-point arithmetic operations
 2.8 Fortran analysis of a floating-point number
 2.9 Calculation of elementary functions
Chapter 3 Surveillance of Number Ranges
 3.1 Introduction
 3.2 Allowable number ranges
 3.3 Basic real arithmetic operations
 3.4 The quadratic equation
 3.5 Complex arithmetic operations
Chapter 4 Solution of Equations
 4.1 Introduction
 4.2 Attainable accuracy
 4.3 Graphical methods
 4.4 The method of bisection
 4.5 The method of false position
 4.6 The secant method
 4.7 General properties of iterative methods
 4.8 Generation of iterative methods
 4.9 The Newton method
 4.10 Muller's method
 4.11 Orders of convergence of iterative methods
 4.12 Acceleration of the convergence
 4.13 Systems of nonlinear equations
Chapter 5 Roots of Polynomial Equations
 5.1 Introduction
 5.2 General properties of polynomials
 5.3 The Newton method and related methods
 5.4 Muller's method and Cauchy's method
 5.5 Location of the roots
 5.6 Root acceptance and refinement
 5.7 Matrix related methods: the modified Bernoulli method
 5.8 Matrix related methods: the IP method
 5.9 Polyalgorithms
 5.10 Other methods
Chapter 6 Interpolation and Approximation
 6.1 Introduction
 6.2 Linear interpolation
 6.3 Convergence and accuracy of linear interpolation
 6.4 Lagrangian interpolation
 6.5 Convergence and accuracy of Lagrangian interpolation
 6.6 Interpolation with equal intervals
 6.7 Hermite interpolation
 6.8 Limitations on polynomial interpolation: smooth interpolation
 6.9 Inverse interpolation
 6.10 Approximation by polynomials
 6.11 Least squares approximation by polynomials
 6.12 Rational approximation
 6.13 Trigonometric interpolation and approximation
 6.14 Interpolation in two variables
Chapter 7 Numerical Differentiation and Quadrature
 7.1 Introduction
 7.2 The method of undetermined weights
 7.3 Numerical differentiation
 7.4 Numerical quadrature--equal intervals
 7.5 The Euler-MacLaurin formula
 7.6 Romberg integration
 7.7 Error determination
 7.8 Numerical quadrature--unequal intervals
Chapter 8 Ordinary Differential Equations
 8.1 Introduction
 8.2 Existence and uniqueness
 8.3 Analytic methods
 8.4 Integral equation formulation--the Picard method of successive approximations
 8.5 The Euler method
 8.6 Methods based on numerical quadrature
 8.7 Error estimation for predictor-corrector methods
 8.8 A numerical example
 8.9 Runge-Kutta methods
 8.10 Methods based on numerical differentiation
 8.11 Higher-order equations and systems of first-order equations
 8.12 The use of high-speed computers
Appendix A  
Appendix B  
Appendix C